Talk:Largest known prime
I have heard about award for finding prime with more than 100 million digit number. Is it possible on the PC (reasonable time), or there need a supercomputer? Ikosarakt1 (talk) 13:12, March 7, 2013 (UTC) The GIMPS program is a distributed project consisting of thousands of computers, with a throughput of about 100 teraflops. It's been running for 17 years. So no, it doesn't seem likely that a single PC working alone will beat them to the punch. (Although $150,000 seems tasty!) Now, the odds of a particular 100-million digit Mersenne candidate being prime is about 1 in 100 million, give or take. But if you got lucky, perhaps a current PC could do a Lucas-Lehmer test in reasonable time. I don't know, haven't done the calculations, although it would be 100 times the time a 10 times the memory required as that of a 10 million digit candidate. The easiest thing to do is join the GIMPS program - it's free, and it runs on your computer downtime. If you find any Mersenne prime, 100 million digit or not, you'll be in line for a reward - although you won't get the full $150,000, even if you find the first 100 million digit prime. Deedlit11 (talk) 15:42, March 7, 2013 (UTC) :For the record, here are the prize distribution rules if you find a new Mersenne prime as a GIMPS participant. --Ixfd64 (talk) 18:33, March 7, 2013 (UTC) Deedlit, I was tried to estimate the number of operations needed to verify that M(332192831) is prime. Since the Lucas-Lehmer test has complexity O(log2 log(n) log(log(n))) for n-th Mersenne number, 332192831-th Mersenne would take 3321928312*log(332192831)*log(log(332192831)) ~ 8.75*1017 (875 quadrillion) operations. But my computer can count only to trillion by a few hours. However, if GIMPS has total productivity of about 100 teraflops, then verification whether M(332192831) is a prime or not spend \(8.75*10^{17} \over 10^{14}\) = 8750 seconds, about 2 hours 26 minutes. So why GIMPS not do that? Ikosarakt1 (talk) 20:00, March 7, 2013 (UTC) :This is because each step of the Lucas-Lehmer test depends on the result of the previous one. As such, it cannot be easily parallelized. --Ixfd64 (talk) 22:48, March 7, 2013 (UTC) :As ixfd64 said, you can't easily distribute the problem over thousands of computers. I don't think that the FFT multiplication is particularly parallelizable either. Also, there's less than a 1 in 100 million chance that 332192831 is the exponent of a Mersenne prime, so you will probably have to test hundreds of millions of candidates before you find one. The GIMPS project took 4 years to find a Mersenne prime in the 13-18 million digit range, and the time required goes up more than the cube of the number of digits (the Lucas Lehmer test is approximately O(n^2), but you need to test O(n) candidates to find a prime), so one would expect finding a 100 million digit prime would take over a hundred years to find. Of course, if they were in it for the money they may as well start testing 100 million digit candidates immediately, rather than waste their time with candidates in the tens of millions now that they have already collected the prize for that. It's probably an academic integrity sort of thing - they want to find the Mersenne primes more or less in order. Deedlit11 (talk) 00:11, March 8, 2013 (UTC) ::The reason they're in only the tens of millions of digits is because they want to exhaustively search all Mersenne primes. Now ALL Mersenne primes are exhausted until M(82E0006). This number will be updated every new M-prime. 17:53, January 5, 2018 (UTC) Supercomputers Why mankind can't request supercomputers for finding large Mersenne primes? I read about 17.59 petaflops-supercomputer, and it turns out that M(332192831) will be verified within 50 seconds on it. Ikosarakt1 (talk ^ ) 13:08, July 7, 2013 (UTC) Because there is no importance with it. It isn't even significant fot maths. We already know there is infinitely many primes, and one more won't prove infinitude of Merssene primes. Of course, we can request it, but I don't think we'll get one. LittlePeng9 (talk) 17:11, July 7, 2013 (UTC) Question In , which one is prime, \(9.19444^{1\,048\,576}\) or \(919\,444^{1\,048\,576}\)? ARsygo (talk) 13:59, April 11, 2018 (UTC) :The latter, plus one. LittlePeng9 (talk) 15:25, April 11, 2018 (UTC)